JOURNAL OF APPLIED PHYSICS
VOLUME 91, NUMBER 1
1 JANUARY 2002
Itinerant metamagnetism and possible spin transition in LaCoO3
by temperatureÕhole doping
P. Ravindran,a) H. Fjellvåg, and A. Kjekshus
Department of Chemistry, University of Oslo, Box 1033, Blindern, N-0315 Oslo, Norway
P. Blaha, K. Schwarz, and J. Luitz
Institut für Physikalische und Theoretische Chemie, Technische Universität Wien, A-1060 Vienna,
Getreidemarkt 9/156, Austria
共Received 29 January 2001; accepted for publication 17 September 2001兲
The electronic structure of the perovskite La1⫺x Srx CoO3 has been obtained as a function of Sr
substitution and volume from a series of generalized-gradient-corrected, full-potential,
spin-density-functional band-structure calculations. The energetics of different spin configurations
are estimated using the fixed-spin-moment 共FSM兲 method. From the total energy versus spin
magnetic moment curve for LaCoO3 the ground state is found to be nonmagnetic with the Co ions
in a low-spin 共LS兲 state, a result that is consistent with the experimental observations. Somewhat
higher in energy, we find an intermediate-spin 共IS兲 state with spin moment ⬃1.2␮ B /%f.u. From the
anomalous temperature dependent susceptibility along with the observation of an IS state we predict
metamagnetism in LaCoO3 originating from an LS-to-IS transition. The IS state is found to be
metallic and the high-spin 共HS兲 state of LaCoO3 is predicted to be a half-metallic ferromagnet. With
increasing temperature, which is simulated by a corresponding change of the lattice parameters, we
have observed the disappearance of the metamagnetic solution that is associated with the IS state.
The FSM calculations on La1⫺x Srx CoO3 suggest that the hole doping stabilizes the IS state and the
calculated magnetic moments are in good agreement with the corresponding experimental values.
Our calculations show that the HS state cannot be stabilized by temperature or hole doping since the
HS state is significantly higher in energy than the LS or IS state. Hence the spin-state transition in
LaCoO3 by temperature/hole doping is from an LS to an IS spin state and the present work rules out
the other possibilities reported in the literature. © 2002 American Institute of Physics.
关DOI: 10.1063/1.1418001兴
I. INTRODUCTION
low-, intermediate- or high-spin state. LaCoO3 itself is a
nonmagnetic insulator at low temperature, usually referred to
as a low-spin 共LS兲 state (S⫽0) because the atomic configu6 0
ration (t 2g
e g ) of Co3⫹ ions has no magnetic moment. Magnetic susceptibility slowly increases with temperature and
reaches a maximum at T⬇90 K. Above this temperature, the
system shows a Curie–Weiss-law behavior, which is followed by a structural transition at 500 K. The origin of the
low-temperature increase in the susceptibility is unclear at
present. It is suggested that this could be due to frozen-in
ferromagnetic domains which are trapped at low
temperatures.4 While it is generally agreed that the lowtemperature phase is a nonmagnetic LS state at high tem4 2
e g ) and an
perature both a high-spin 共HS兲 state5–10 (S⫽2, t 2g
5 1
11,12
intermediate-spin 共IS兲 state
(S⫽1, t 2g e g ) have been proposed for LaCoO3 high temperature. Most previous studies
have treated the spin-state transition at 90 K as a transition
from the LS state to a thermally excited HS state,7 which is
reported13 to be only 10– 80 meV higher in energy than the
LS state.
The attempts to explain the spin-state transition in
LaCoO3 based on different experimental techniques is rather
controversial. Direct magnetic measurements allow one to
unambiguously identify the LS state in the temperature range
below 50 K.6,3,14 –16,12,17 The behavior of the magnetic sus-
The coupling of the charge to the spin and lattice degrees
of freedom yields interesting phenomena such as the colossal
magnetoresistance1 and high-temperature superconductivity2
where the underlying mechanism is still under investigation.
In the La1⫺x Srx CoO3 perovskite phase, cobalt spin configurations change with temperature and Sr concentration giving
a rich variety of magnetic and transport properties that has
attracted considerable attention over the last 4 decades. The
simultaneous presence of strong electron–electron interaction within the transition-metal cobalt 3d manifold and a
sizable hopping-interaction strength between the 3d and
oxygen 2p states are primarily responsible for the wide
range of properties exhibited by these compounds. LaCoO3
is unique in that it is a diamagnetic semiconductor3 with a
spin gap of 30 meV, a charge gap of 0.1 eV and a rhombohedrally distorted perovskite structure at low temperature. It
undergoes a spin-state transition from a diamagnetic state to
a paramagnetic state with a finite moment at 100 K and from
semiconductor to metal above ⬃500 K.3
The magnetic properties of the cobaltites depend on the
spin state of Co3⫹ and Co4⫹ , i.e., whether they are in the
a兲
Author to whom correspondence should be addressed; electronic mail:
ravindran.ponniah@kjemi.uio.no
0021-8979/2002/91(1)/291/13/$19.00
291
© 2002 American Institute of Physics
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292
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
ceptibility at low temperature, in the region around 100 K,
has been understood in terms of thermal activation of a magnetic HS state from the LS ground state.6,14,18 Raccah and
Goodenough7 have emphasized that more complex supercell
structures play an important role in the spin-state transition
and reported the coexistence of LS and HS states of cobalt in
LaCoO3 and a first-order phase change at 1210 K. Rodriguez
and Goodenough19 have suggested from magnetic and transport measurements that LaCoO3 is in an LS state below 35
K, an LS–HS disordered state between 35 and 110 K, an
LS–HS ordered state between 110 and 350 K, and an IS–HS
ordered state above 650 K. However, a careful powder neutron diffraction study20 found no evidence for any static ordering of distinct Co sites. Abbate et al.9 have interpreted the
transition in the range 400– 650 K as being due to an LSto-HS transition, based on x-ray absorption and x-ray photoelectron spectroscopy measurements. Saitoh et al.12 have argued that the 100 K transition is most likely due to an LSto-IS transition, and also suggested that the 500 K transition
is due to the population of the HS state. The XPS spectra of
LaCoO3 at room temperature and 573 K along with ionic
multiplet analysis suggest21 that the LS and HS states coexist
at room temperatures. Polarized neutron scattering
measurements8 exhibit two magnetic–electronic transitions:
one near 90 K and another near 500 K. The spin-state transition is maintained to occur at low temperature, and the high
temperature transition is not dominantly of magnetic origin.
NMR22 studies also claim that the LS-to-HS spin state transition occurs at ⬃90 K. Co-K extended x-ray absorption fine
structure measurements23 established the occurrence of two
cobalt sites above 400 K and this may be associated with two
spin states for Co. Madhusudan et al.24 reported that the series RCoO3 共R⫽Pr, Nd, Tb, Dy and Yb兲, all exhibit the considered LS-to-HS state transition of cobalt. Taguchi25 has
shown from structural and susceptibility studies that Co3⫹ in
Nd共Cr1⫺x Cox )O3 is in the low-spin state at low temperature
and transforms to a mixed-spin state with increasing temperature. From temperature-dependent susceptibility and
Knight-shift measurements26 it has been pointed out that the
LS–HS model is not applicable for understanding the spinstate transition in LaCoO3 and thus a LS–IS model is more
appropriate. Heikes et al.5 considered an IS state to account
for the effective moment obtained from susceptibility data
below the ⬃500 K transition in LaCoO3 . From photoemission measurements it has been concluded that the hybridization of oxygen 2p orbitals and cobalt 3d states stabilizes the
IS state with spin S⫽1.27 Heat capacity measurements also
support the LS-to-IS state transition.28 Recent magnetic susceptibility and neutron-diffraction studies29 show that
LaCoO3 has the LS Co3⫹ configuration at the lowest temperatures. Below 350 K IS remains isolated and localized;
above 650 K, all the trivalent Co ions are transformed to the
IS state with itinerant d electrons.
Several theoretical attempts have also been made to understand the microscopic origin of the spin-state transition in
LaCoO3 . From an LDA⫹U approach 共where U is the onsite Coulomb interaction兲 Korotin et al.11 have demonstrated
that the IS state is relatively stable over the HS state, as a
result of the strong p – d hybridization effect as well as of the
Ravindran et al.
orbital ordering effect. They have also explained the semiconducting behavior above the 100–500 K region as a spatial
ordering of orbitals associated with a Jahn–Teller distortion
of an IS state and the thermal disordering of this state results
in a gradual crossover to the metallic state at high temperatures. However, a controversy still exists since the calculation of Mizokawa and Fujimori30 did not find the orbitalordered state. Recent neutron diffraction measurements31
also give no evidence for orbital ordering. The Hartree–Fock
calculations on the multiband lattice model30,32 have also
shown that the IS state is more stable than the HS state.
Simulations using molecular-orbital dynamics33 show that
magnetoelastic coupling plays a very important role, the
spin-state transition being mainly induced by variation of the
Co–O bond length with temperature. Liu et al.34 have suggested that there is a thermodynamic equilibrium between
6 1
5 0
e g ) and Co4⫹ (t 2g
e g ) in
LS Co3⫹ , HS Co3⫹ , Co2⫹ (t 2g
LaCoO3 . The recent calculations35 within the unrestricted
Hartree–Fock approximation and a real space recursion
method suggest that the spin-state transition at 90 K takes
place from the LS to LS–HS ordered state. Mizokawa and
Fujimori36 showed from unrestricted Hartree–Fock calculations that the LS state is the ground state and the IS state is
the first excited spin state. The analysis of the core-level
spectrum in terms of a configuration interaction model suggests that both LS and HS states coexist at low temperature
共100 K兲, but at 573 K there is a decrease in the LS contribution related to local structural changes.37
Much of the difficulty in reaching a consensual interpretation originates from the traditional use of an ionic, ligandfield model. In such a picture, only two distinct spin states of
Co3⫹ are energetically operational.38 Also most of the calculations presented in the literature dealing with spin-state transition involve only a few adjustable parameters. In order to
obtain a better understanding of both the spin-state transition
in LaCoO3 and the origin of the paramagnetic state with
local magnetic moments, it is necessary to examine the energetics of various spin-ordered states as a function of hole
doping/temperature. This is the motivation for the present
study.
The discovery of colossal magnetoresistance 共CMR兲 in
manganites with perovskite structure39 has stimulated research of compounds exhibiting large magnetoresistance.
Fairly large magnetoresistance has indeed been observed in
the perovskite series La1⫺x Ax CoO3 共A⫽Ca, Sr, or Ba兲.40
The magnetic and transport properties of La1⫺x Srx CoO3 and
CMR materials such as La1⫺x Srx MnO3 have common
features.7,41– 43,19 In both systems the substitution of La with
a divalent ion creates a metallic ferromagnetic state. The
ferromagnetic interactions between Co3⫹ and Co4⫹ are supposed to arise from a double exchange mechanism like that
in La1⫺x Srx MnO3 materials. However, the detailed mechanism of the ferromagnetism and the metal–insulator transition in cobaltites are not well understood. In metallic
samples of La1⫺x Srx CoO3 (x⬎0.2) the magnitude of the
magnetoresistance is typically small whereas it becomes
larger in the composition range x⭐0.2, where the system is
close to a metal–insulator transition.44
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J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
The magnetic state of La1⫺x Ax CoO3 strongly depends
on the doping concentration x. Jonker and van Santen45 studied La1⫺x Srx CoO3 in 1953 by magnetization measurements
and reported ferromagnetic order for an intermediate Sr concentration. They argued that the double-exchange
Co3⫹ – Co4⫹ interaction is responsible for the ferromagnetism. Bhide et al.46 measured the temperature dependence
of Mössbauer spectra for ferromagnetic La1⫺x Srx CoO3 (0
⭐x⭐0.5) and reported that ferromagnetic Sr-rich clusters
coexist with paramagnetic La-rich regions in the same phase.
The 3d holes created by the Sr substitution are itinerant both
above and below the Curie temperature T C and all the experimental results are explained on the basis of itinerantelectron ferromagnetism. Itoh et al.43 studied this system by
magnetization measurements at low fields and obtained a
phase diagram with a paramagnetic-to-spin-glass-transition
for x⬍0.18 and a paramagnetic-to-cluster-glass transition for
x⭓0.18. Neutron diffraction measurements47 showed the appearance of magnetic peaks below T C corresponding to longrange ferromagnetic order for x⭓0.2.
Using the unrestricted Hartree–Fock approximation and
a real-space-recursion method, Zhuang et al.48 calculated
different magnetic phases for SrCoO3 and concluded that
4 1
e g ) state. The observed spin moment
SrCoO3 is in the IS (t 2g
in La0.7Sr0.3CoO3 from neutron diffraction studies49 has concluded that the system will have Co4⫹ in the LS state and a
mixed LS and HS configuration for Co3⫹ . The magnetic
state of La1⫺x Ax CoO3 was suggested to be a mixture of HS
5 0 50
e g ), because the measured saturaCo3⫹ and LS Co4⫹ (t 2g
tion magnetic moment is only about half of the moment for
HS Co3⫹ . 50,45 From application of the numerically exact diagonalization method on Co2 O11 clusters it has been shown
that a coexistence of HS and IS due to strong p – d mixing is
most plausible in doped cobaltites.51 However, our recent
electronic structure calculations on La1⫺x Srx CoO3 with the
supercell approach suggest that Co ions close to both La and
Sr are in the IS state. In the present article we report on the
energetics of various spin states of Co ions as a function of
hole doping and volume in LaCoO3 . Based on these results
we will consider the possible spin-state transition in LaCoO3
on temperature and hole doping.
The rest of this article is organized as follows. In Sec. II,
we describe the computational procedure used in the present
calculations. In Sec. III, we discuss the electronic structure
and magnetic properties of LaCoO3 as a function of Sr substitution and volume from the results obtained from virtual
crystal approximation 共VCA兲 and supercell calculations using the fixed-spin-moment method. Finally in Sec. IV the
findings of the present study are summarized.
II. COMPUTATIONAL DETAILS
A. Linearized-augmented plane wave „LAPW…
calculations
The present investigation is based on ab initio electronic
structure calculations derived from spin-polarized, densityfunctional theory 共DFT兲. In particular we have applied the
full-potential linearized-augmented plane wave 共FPLAPW兲
method as embodied in the WIEN97 code52 using the scalar-
Ravindran et al.
293
relativistic version without spin-orbit coupling. The charge
density and the potentials are expanded into lattice harmonics up to L⫽6 inside the spheres and into a Fourier series in
the interstitial region. We have included the local orbitals53
for La 5s,5p, Sr 4s,4p, Co 3p and O 2s. The effects of
exchange and correlation are treated within the generalizedgradient-corrected local spin-density approximation using
the parameterization scheme of Perdew et al.54 We have carried out test calculations with different sets of k points and
found that the fixed-spin-moment 共q兲 共FSM兲 curve changes
considerably with the number of k points. For example,
when we use only four k points in our calculations we obtained the ferromagnetic state lower in energy than the nonmagnetic state. To ensure convergence for the Brillouin zone
integration 110 k points in the irreducible wedge of the first
Brillouin zone 共IBZ兲 were used for the rhombohedral structure and 84 k points in IBZ for the cubic phase 共even half the
number of these k points gave the correct result qualitatively兲. A similar density of k points was used in the supercell calculations. Self-consistency was achieved by demanding the convergence of the total energy to be smaller than
10⫺5 Ry/cell. This corresponds to a convergence of the
charge to below 10⫺4 electrons/atom. For all calculations the
ratio between the sphere radii used are 1.25, 0.88, and 1.25
for R La /R O , R Co /R O , and R Sr /R O , respectively, where R O
⫽1.8 bohr. Since the spin densities are well confined within
a radius of about 1.5 bohr, the resulting magnetic moments
do not depend strongly on variation of the atomic sphere
radii.
B. The fixed-spin-moment „FSM… method
Conventional spin-polarized calculations based on DFT
allows the moment to float and the ground state is obtained
by minimizing the energy functional, E, with respect to the
charge and magnetization densities ␳ (r) and m(r) under the
constraint of a fixed number of electrons N. With the variational principle this corresponds to minimizing the functional
F 关 ␳ 共 r 兲 ,m 共 r 兲兴 ⫽E 关 ␳ 共 r 兲 ,m 共 r 兲兴 ⫺ ␮
冋冕
册
␳ 共 r 兲 dr⫺N , 共1兲
where ␮ is the chemical potential. The minimization gives
␦ E/ ␦ ␳ (r) ⫽ ␮ , ␦ E/ ␦ m(r) ⫽0, leading to effective oneelectron equations which are solved by a self-consistent procedure that determines the moment which minimizes the total energy. In cases where two 共or more兲 local minima occur
for different moments, conventional spin-polarized calculations become difficult to converge or ‘‘accidently’’ converge
to different solutions. Although LaCoO3 is a nonmagnetic
material, our conventional spin-polarized calculations always
converged to a ferromagnetic solution with a moment of 1.2
␮ B /f.u.
In order to reach convergence or to study spin fluctuations it is advantageous to calculate the total energy as a
function of magnetic moment using the so-called fixed-spinmoment method.55–57 In this method one uses the magnetic
moment M as an external parameter and calculates the total
energy as a function of M. In general one must release the
constraint that the Fermi levels for up and down spins are
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294
Ravindran et al.
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
equal because the equilibrium condition is not satisfied for
arbitrary M. The number of valence electrons N is known
and M is fixed 共as input parameter兲 determining the values
for E F↑ and E F↓ from
N⫽N ↑ ⫹N ↓ ⫽
冕
↑
EF
⫺⬁
D ↑ 共 E 兲 dE⫹
冕
↓
EF
⫺⬁
D ↓ 共 E 兲 dE
共2兲
M ⫽N ↑ ⫺N ↓ ,
共3兲
where D ↑ (E) and D ↓ (E) are the spin-up and spin-down
DOS, respectively. At maxima and minima of the FSM
curve, the two Fermi levels are equal, i.e., E F↑ ⫽ E F↓ . In the
FSM method Eq. 共1兲 is modified to minimize the functional
F 关 ␳ 共 r 兲 ,m 共 r 兲兴 ⫽E 关 ␳ 共 r 兲 ,m 共 r 兲兴 ⫺ ␮
⫺h
冋冕
冋冕
册
␳ 共 r 兲 dr⫺N
册
共4兲
m 共 r 兲 dr⫺M ,
where h is the Lagrange multiplier which applies to the constraint of having a fixed spin moment M. The orbital contributions to the magnetization are neglected, since they are
usually small for 3d transition-metal phases. Instead of minimizing with respect to ␳ (r) and m(r), it is more illustrative
to change the spin-up ␳ ↑ (r)⫽ 21 关 ␳ (r)⫹m(r) 兴 , and spindown ␳ ↓ (r)⫽ 21 关 ␳ (r)⫺m(r) 兴 densities. Then the variational
principle yields ␦ E/ ␦ ␳ ↑ (r) ⫽ ␮ ⫹h and ␦ E/ ␦ ␳ ↓ (r) ⫽ ␮
⫺h. ␮ ⫾h may be identified as the chemical potentials for
the two different spins. Thus, the condition of having a fixed
spin moment corresponds to using two different chemical
potentials, i.e., two Fermi energies for one material at zero
temperature. This can also be seen by rewriting Eq. 共4兲 as
F 关 ␳ 共 r 兲 ,m 共 r 兲兴 ⫽E 关 ␳ 共 r 兲 ,m 共 r 兲兴 ⫺ 共 ␮ ⫹h 兲
册
⫺N ↑ ⫺ 共 ␮ ⫺h 兲
冋冕
冋冕
␳ ↑ 共 r 兲 dr
册
␳ ↓ 共 r 兲 dr⫺N ↓ . 共5兲
Therefore, the FSM method corresponds to fixing the number of electrons of the two spins separately. Given N and M,
N ↑ and N ↓ are defined from Eqs. 共2兲 and 共3兲. The associated
Fermi energies are then found from the relations
N ␴⫽
冕
␴
EF
⫺⬁
D ␴ 共 E 兲 dE,
共6兲
where D ␴ (E) and E F␴ are the density of states and the Fermi
energy for spin ␴ , respectively. Extensive FSM calculations
have been undertaken to theoretically find the stability condition for 3d and 4d magnetic materials.57– 61 Similar calculations are also extensively used to explain the magnetovolume instabilities in Invar alloys.62
C. Structure
LaCoO3 has a rhombohedrally distorted pseudocubic
perovskite structure. The space group is R3̄c and each unit
cell contains 2 f.u. La1⫺x Srx CoO3 has the rhombohedral
structure with space group R3̄c in the range 0⭐x⭐0.5 and
transforms to a cubic phase with the space group Pm3̄m at
higher Sr contents. The rhombohedral distortion decreases
with the increase of x. A similar variation results from thermal expansion for the parent LaCoO3 . The oxygen atoms are
in the 6e ( 41 ⫺ ␦ x, 14 ⫹ ␦ x, 14 ) Wykoff position with ␦ x
⫽0.0522. Using the force minimization method we have optimized ␦ x and found an optimized value of 0.0638. The
FSM calculations at low temperature are made with this
value for ␦ x and the experimental lattice parameters corresponding to 4 K. The structural parameters for the holedoped systems used in the present calculations are the same
as those used in Ref. 63. The spin-state transition probably
occurs mainly due to the larger variation of the Co–O bond
length with increasing temperature.7,33 Hence, it is interesting to study the spin-state transition as a function of lattice
parameters and we have performed FSM calculations for
LaCoO3 with lattice parameters corresponding to 4 K as well
as 1248 K. The structural parameters at 1248 K were taken
from high-resolution powder-diffraction measurements.20
D. Substitution
The hole-doping effect in LaCoO3 has been simulated
using supercell calculations as well as VCA calculations. For
the VCA calculation we have taken into account the experimentally reported49 structural parameter changes as a function of Sr substitution. Hence, these calculations accounted
properly for the hybridization effect. In this approximation
the true atom in the material is replaced by an ‘‘average’’
atom which is interpolated linearly in charge between the
corresponding pure atoms. In the VCA calculations the
charge-transfer effect is not thoroughly accounted for,
whereas the band-filling effects are properly taken into account. The chosen approximation has an advantage owing to
its simplicity and hence we are able to study small concentrations of Sr in LaCoO3 . However, for 50% Sr substitution
we have made explicit supercell FSM calculations.
III. RESULTS AND DISCUSSION
Our current results are based on total-energy FPLAPWband calculations utilizing the FSM procedure. We have considered only the ferromagnetic state. Each point on the E(M )
curves shown in Fig. 1共a兲 is derived from a band calculation
in which the total moment of the phase was constrained to a
given M value. The FSM procedure fixes only the total moment and not the local moments. The latter are free to take
whatever value that minimizes the energy. In all cases, the
local moments vanish at M ⫽0; i.e., the situation M ⫽0 is
never produced by a cancellation of opposite local moments.
A. DOS characteristics
The calculated DOS for LaCoO3 are shown in Fig. 2 for
the three spin arrangements LS, IS and HS. First of all, the
results predict a metallic behavior for the LS state 关Fig. 2共c兲兴
of LaCoO3 , but the total DOS has a sharp minimum at E F .
This is in contrast to the semiconducting behavior observed
experimentally.41 This kind of discrepancy may be expected
in narrow-band materials due to the correlation effect. However, this does not hold in the present case as our recent
optical property calculations for LaCoO3 show good agree-
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J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
FIG. 1. The total energy of LaCoO3 as a function of constrained spin moment obtained for 共a兲 volume corresponding to 4 K. The zero level is chosen
at the nonmagnetic energy minimum. The inset gives an enlargement for the
energy interval close to IS. The extrapolation of the metastable state above
25 meV is indicated by the straight line. Vertical dashed lines represent the
crossover to IS and HS and the corresponding temperatures required to
excite the system to these states are quoted. 共b兲 The same for a volume
corresponding to 1248 K.
ment with experimental spectra up to 25 eV. Hence, the metallic behavior in LaCoO3 is due to the usual underestimation
of the band gap in LDA and not to the correlation effect. We
have recently reported63 on the bonding behavior of
La1⫺x Srx CoO3 and found indications of strong covalent hybridization between O p and Co d in this phase. For a more
detailed discussion about the bonding behavior reference is
made to the preceding communication.63 The O p and Co d
states are mixed with each other in the valence band. By
contrast, the La spectral weight contributes mainly to the
unoccupied electronic states in the conduction band. This
suggests that La has more ionic character and is stabilized by
the Madelung potential, whereas the covalent contribution to
the bonding is more prominent within the Co–O octahedra.
The sharp feature at 4 eV above the Fermi level corresponds
to the La 4 f band and the DOS segment at 4 – 8 eV is composed mainly of La 5d states.
The Co 3d states are very important and deserve to be
discussed in more detail because they determine the magnetic properties. LaCoO3 has a pseudocubic perovskite structure with a rhombohedral distortion along the 共111兲 direction.
Ravindran et al.
295
FIG. 2. Total DOS for LaCoO3 in the LS, IS, and the HS states obtained for
the volume corresponding to 4 K. The Fermi level is marked with the vertical line at zero energy.
Since the rhombohedral distortion is small, we use the concept of t 2g and e g orbitals 共as referred to in the cubic situation兲 in the following discussion. In an octahedral crystal
field the d electrons will be split into double degenerate e g
and triple degenerate t 2g states. The t 2g and e g projected
density of states of Co in the cubic phases of LaCoO3 and
SrCoO3 are given in Fig. 3 for the nonspin-polarized and
ferromagnetic cases. The large peak below the Fermi level
corresponds to the Co t 2g bands. These relatively nonbonding states produce weak Co–O–Co interactions which give
rise to a narrow band. By contrast, the Co e g states produce
very strong Co–O–Co interactions which give rise to a much
larger dispersion, and result in the broader e g band observed
for both LaCoO3 and SrCoO3 . When the spin polarization is
included in the calculations, the t 2g states for the majority
spin become localized compared with the nonspin-polarized
case and thus the total energy calculation shows that the
ferromagnetic state is lower in energy than the nonmagnetic
case.63 However, for the minority-spin state in Fig. 3共a兲 E F is
located at a sharp nonbonding t 2g peak. As this is not a
favorable condition for stability, a rhombohedral distortion
arises due to a Jahn–Teller/Peierls-like instability.
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296
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
Ravindran et al.
FIG. 3. The e g and t 2g splitted Co d DOS for: 共a兲 cubic LaCoO3 and 共b兲
cubic SrCoO3 with and without spin polarization.
The simple ligand model predicts that for the LS state of
LaCoO3 , the t 2g levels are completely filled and the e g states
completely empty. In our calculation, however, the e g states
are distributed over the entire valence and conduction bands.
The band structure obtained from a tight-binding method64
also shows that the e g orbitals partly fall below the Fermi
level and are mixed with the t 2g orbitals. This feature can be
understood as follows. The lobes of the t 2g orbitals point
between the oxygen ligands, whereas the e g orbitals point
directly toward the ligands. Hence, the overlap with O 2p
orbitals will be greater for the e g states, and the increased
overlap results in local repulsion between overlapping charge
densities. This repulsive interaction pushes the e g orbitals to
higher energy. However, some of the repulsion is compensated by hybridization in the resulting bonding states, which
in turn leads to a considerable amount of e g state in the
conduction band. The calculations show that E F lies in the
vicinity of the sharp nonbonding t 2g peak for the Co 3d
electrons of the ground state LS configuration. In this case, a
small shift in E F leads to large changes in N(E F ) and causes
the ferromagnetic instability of the system. So, the presence
of the high DOS close to E F and the small energy difference
between the nonmagnetic and ferromagnetic state are the two
main reasons for the temperature induced anomalies in the
physical properties.
Considering DOS for LaCoO3 in the rhombohedral
structure and the LS state, it is interesting to note that E F lies
in a pseudogap which separates bonding from antibonding
states. As a result there is a gain in one-electron energy and
FIG. 4. The calculated FSM curves for the cubic phase of: 共a兲 SrCoO3 , 共b兲
La0.5Sr0.5CoO3 , and 共c兲 LaCoO3 .
the system stabilizes in the rhombohedrally distorted nonmagnetic phase. In the case of SrCoO3 , the 3d DOS of Co in
the nonspin-polarized case shows that E F lies in a sharp peak
which originates from nonbonding t 2g states. Using the calculated N(E F )⫽12.09 states/eV and the Stoner I value65 of
0.4898 eV the calculated Stoner product of 5.9 indicates that
the Stoner criterion is fulfilled in SrCoO3 and hence the ferromagnetism appears. In the spin-polarized case these t 2g
states are exchange splitted as shown in Fig. 3共a兲. Unlike
LaCoO3 the Co 3d t 2g states for spin-polarized SrCoO3 are
well separated from E F , hence stabilizing the ferromagnetic
state. This is evident from the FSM curve for SrCoO3 shown
in Fig. 4 where the ferromagnetic state with a magnetic moment of 2.6 ␮ B /f.u. is 0.463 eV lower in energy than the
nonmagnetic state. Even though SrCoO3 is stabilized in the
cubic ferromagnetic phase, our calculation shows that E F
falls on a shoulder of the nonbonding minority spin Co t 2g
DOS. This may be one reason for the presence of oxygen
vacancies in SrCoO3 .
The pseudogap feature in the vicinity of the Fermi level
disappears in the IS and HS state of LaCoO3 as shown in
Figs. 2共a兲 and 2共b兲, respectively. In Fig. 1共a兲 the limits of the
IS and HS states are represented by vertical lines. A detailed
examination of energy versus moment shows that the slope
changes its sign around 1 ␮ B . However, a flattened region is
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Ravindran et al.
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
297
TABLE I. Magnetic moments in ␮ B /Co for La1⫺x Srx CoO3 obtained by
FSM calculations 共Theory兲 compared with experimental neutron scattering
values 共Exp.兲, together with values obtained for LS, IS, and HS configurations using an ionic model.
FIG. 5. FSM curves for La1⫺x Srx CoO3 (x⫽0 – 0.5) obtained by VCA calculation.
seen in the vicinity of 1.2 ␮ B 关Fig. 5 and the inset to Fig.
1共a兲兴 where the ferromagnetic state becomes stabilized according to our ferromagnetic spin-polarized calculations. So,
we assigned a moment of 1.2 ␮ B to the IS state. From our
calculations the IS state turns out to be metallic which is
consistent with the LDA⫹U calculation11 that leads to a
half-metallic ferromagnet. Moreover our calculation predicts
the HS state to be a half-metallic ferromagnet, whereas according to LDA⫹U calculations it should be a semiconductor. The reason for the metallic behavior of the IS state is that
the bands formed by e g orbitals are broad and the band splitting is not strong enough to create a gap. On the other hand,
in the HS state, the e ↑g band becomes completely filled and a
band gap appears in the majority-spin state. DOS for the IS
and HS states shows that the nonbonding t 2g electrons are
present at E F in the minority-spin state. Consequently these
states are at a energetically higher level than the LS state
关Fig. 1共a兲兴. The magnitude of DOS just below the Fermi
level is lower for the IS and HS phases than for the LS phase.
A similar decrease is observed with increasing values of x in
the XPS spectra.66 In relation to Fig. 1共a兲 it should be noted
that the one electron eigenvalue sum itself explains why the
LS state is lower in energy than the IS and HS states.
B. Hole doping effect
It has been reported that the La1⫺x Srx CoO3 phase develops a ferromagnetic long-range order above x⫽0.05 and that
the metal–insulator transition takes place at x⬇0.2. 45,67,46
Optical measurements68 show that the electronic structure of
Composition
LS
IS
HS
Exp.
Theory
LaCoO3
La0.9Sr0.1CoO3
La0.8Sr0.2CoO3
La0.7Sr0.3CoO3
La0.6Sr0.4CoO3
La0.5Sr0.5CoO3
SrCoO3
0
0.1
0.2
0.3
0.4
0.5
1
2
2.1
2.2
2.3
2.4
2.5
3
4
4.1
4.2
4.3
4.4
4.5
5
0
—
1.5
1.65
1.85
2.2
1.8
0
1.42
1.57
1.67
1.86
1.98
2.60
the high-temperature metallic state of LaCoO3 is very similar
to that of the doping-induced metallic state. Hence, the FSM
calculations on hole-doped LaCoO3 are expected to give a
better understanding about the nature of the temperatureinduced spin-state transition.
For the Sr-doped system, it is natural that the Sr substitution induces a partial oxidation from Co3⫹ to Co4⫹ . From
the effective magnetic moment obtained by magnetization
measurements, Taguchi and Shimada50 concluded that Co3⫹
is in an HS state in La1⫺x Srx CoO3 and Co4⫹ in an LS state
because the saturation moment in the ferromagnetic phase
(0.3⬎x) is only about half the full moment of HS Co3⫹ . 45,50
A transition from LS to HS through doping has been suggested from NMR studies22 on 59Co and 139La probes and
neutron scattering.8 Electron spectroscopy66 and magnetic
measurements45,67 indicate that hole doping leads to the formation of HS rather than LS configuration. As the radius of
Sr2⫹ is larger than that of La3⫹ , it is suggested that the Sr
doping favors the HS state by the introduction of
Co4⫹ (3d 5 ). 69 The HS state of Co3⫹ possesses S⫽2, viz. a
maximum magnetic moment of ␮ Co⫽4 ␮ B . This corresponds to the purely ionic model; hybridization of Co 3d
orbitals with the O 2p orbital and the band formation in the
solid states can significantly renormalize this ionic value.
Hence, the calculated magnetic moments are always smaller
than the ionic values 共Table I兲, and much smaller than the HS
ionic value indicating that this discrepancy cannot be accounted for as a hybridization effect. It should be noted that
one can expect a discrepancy between experiment and theory
above x⬎0.5, where the oxygen deficiency is known to increase significantly 共see the discussion in Ref. 63兲.
Recent neutron diffraction studies29 show that the doping
with Sr introduces LS Co4⫹ (t 5 e 0 ) which in turn stabilizes
IS Co3⫹ on the neighbors. Ferromagnetic resonance measurements suggest that subjected to hole doping, the cobalt
ions transform from a paramagnetic LS to a ferromagnetic IS
state.42 Ganguly et al.70 concluded from magnetic susceptibility studies that the Co ions in La0.5Sr0.5CoO3 are in the IS
state. Photoemission and x-ray absorption spectroscopic
measurements combined with configuration cluster-model
calculations led Saitoh et al.71 to suggest that it is the Co
ions in the IS state which are responsible for the ferromagnetism in La1⫺x Srx CoO3 . If both Co3⫹ and Co4⫹ are in the
IS states in La0.5Sr0.5CoO3 , one should expect 2.5 ␮ B /f.u.
according to an ionic picture. As in our previous study63 共that
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298
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
indicated strong covalent bonding between Co and O兲, we
obtained 1.98 ␮ B /f.u. for La0.5Sr0.5CoO3 共Table I兲. The FSM
curves from the VCA calculations 共Fig. 5兲 as well as the
supercell calculations 共Fig. 4兲 give similar results. One of the
reasons for the stabilization of the IS state by hole doping is
that the hole doping reduces the ionicity and enhances the
covalent hybridization between Co and O. The observed stabilization of the IS state in hole-doped LaCoO3 is also consistent with recent magnetic and transport property
measurements.72 Comparison between the experimental Co
2p x-ray absorption spectra and atomic-multiplet calculations also indicate that the ground state of SrCoO3 is IS
4 1 27
e g ). For IS Co4⫹ one expects 3 ␮ B /atom. But the hy(t 2g
bridization effect reduces the magnetic moment and hence
we obtain a value of 2.6 ␮ B /f.u. for SrCoO3 .
Early studies led to the suggestion that, in the doped
samples, a paramagnetic La3⫹ region coexists with ferromagnetic Sr2⫹ -rich clusters in the same crystallographic
phase, the ferromagnetic component increasing with x.67 The
magnetic and transport properties of hole-doped LaCoO3
suggest19 that upon Sr doping, the material segregates into
hole-rich, metallic ferromagnetic regions and a hole-poor
matrix similar to LaCoO3 . The Co ions of the ferromagnetic
phase are in an IS configurations, the hole-poor region experiences a thermally induced LS-to-HS transition. A clusterglass state in the region 0.3⬍x⬍0.5 is also proposed43 from
magnetization measurements. For lower Sr contents (x
⬍0.2), the magnetization measurements have clarified a
spin-glass ground state,43,8 where a strong ferromagnetic
short-range correlation is observed by paramagnetic neutron
scattering experiments.8 Our spin-polarized, supercell calculations for La0.75Sr0.25CoO3 show that the cobalt ions closer
to Sr and La give significant magnetic contributions. The
calculated magnetic moment for these two kinds of Co ions
do not differ much, indicating that the spin state of these ions
are almost the same and that the hole doping affects almost
uniformly all the Co ions in the structure.
From the FSM curve obtained as a function of x 共Fig. 5兲,
it is clear that the LS phase of Co3⫹ is the most stable among
the magnetic configurations for x⫽0, but the LS state is
found to be unstable with increasing values of x. This is
consistent with the results obtained within the HF
approximation.32 Further, the instability of the nonmagnetic
phase on hole doping is consistent with the experimentally
observed paramagnetic behavior of the susceptibility for x
⭓0.08. 8 Hole doping in the LS ground state of pure LaCoO3
probably leads to the formation of localized magnetic polarons with unusually high spin numbers (S⫽10– 16). 3 For
La1⫺x Srx CoO3 , it has been reported that the spin-state transition around 90 K disappears with increasing x and the Co
ions are in a magnetic state down to the lowest
temperatures.67 Our calculated results are consistent with
these observation in the sense that the metastable state of
LaCoO3 disappears and a magnetic phase appears on hole
doping.
The total DOS for LaCoO3 in the LS state 关Fig. 2共c兲兴
shows that E F is located in a deep valley, viz. in a nonmagnetic state. The hole doping shifts E F to the peak on the
lower energy side of DOS 共Fig. 6兲. As a result the Stoner
Ravindran et al.
FIG. 6. Co d DOS in La1⫺x Srx CoO3 as a function of x obtained from spinpolarized VCA calculation. For clarity the DOS curves are systematically
shifted 2 states eV⫺1 atom⫺1 in both spin channels for each increment of 0.1
in x, and the DOS maxima are cut at 4 states eV⫺1 atom⫺1 .
criterionfor band ferromagnetism is fulfilled and magnetism
appears. From Fig. 6 it is seen that the overall topology of
the DOS curve does not change significantly on hole doping.
This indicates that the band-filling effect plays a decisive
role for the changes in the magnetic properties of
La1⫺x Srx CoO3 as a function of x. The equilibrium spin moment for La1⫺x Srx CoO3 as a function of x, calculated according to FSM-VCA, is compared with experimental
data73,19 and the results obtained by self-consistent fullpotential-linear-muffin-tin orbital 共FPLMTO兲 supercell calculations in Fig. 7. It should be noted that the calculated
equilibrium magnetic moments seen from the FSM curves
共Fig. 5兲 are in excellent agreement with the experimental
findings as well as our previous FPLMTO results. This indicates that the FSM method is reliable to give correct predictions for equilibrium magnetic phases. The observation of
ferromagnetism in LaCoO3 by temperature/hole doping has
been interpreted as originating from one of the mechanisms:
共i兲 Ordering of HS and LS Co ions through ferromagnetic
superexchange via the intervening oxygens;50 共ii兲 Zener
double
exchange;74
or
共iii兲
itinerant-electron
ferromagnetism.46,75 Our band-structure calculations are able
to explain the magnetic properties indicating that itinerant-
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Ravindran et al.
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
FIG. 7. Calculated magnetic moments for La1⫺x Srx CoO3 versus x obtained
by supercell and VCA calculations from the generalized-gradient-corrected
relativistic full-potential linear muffin-tin orbital method and from FSM
calculations according to the FPLAPW method. Experimental magnetic moments are taken from neutron-scattering measurements 共Ref. 73兲 at 4.2 K
and magnetization measurements 共Ref. 19兲 at 5 K.
band picture 共iii兲 is suitable for these materials. The increasing trend of magnetic moment as a function of hole doping
originates for two reasons. First, owing to band-filling effects
the hole doping moves the Fermi level to the sharp t 2g peak
and thus enhances DOS at the Fermi level as well as the
exchange splitting. Second, an effect of reduced hybridization resulting from the fact that Sr2⫹ is larger in size than
La3⫹ and the consequent expansion in lattice on increasing
substitution. As a result the bands narrow which in turn enhances the spin polarization.
C. Metamagnetism
A metamagnetic transition refers to paramagnetic metallic materials which are rendered ferromagnetic by applying a
sufficiently large external magnetic field. Such a possibility
was first discussed by Wohlfarth and Rhodes76 and later extended by Shimizu.77 Phenomena related to band metamagnetism are observed mainly in Co-based materials such as
pyrite-type phases CoS2 78 Co共Se,S兲2 , 79 Laves-type phases
YCo2 , 80 ScCo2 , 81 LuCo2 , 82 hexagonal Fe2 P-type phases
Co2 P, CoNiP and orthorhombic Co2 P-type83 phases CoMP
共M⫽Mo and Ru兲. Metamagnetism has also been found
experimentally84 and theoretically85 in UCoAl.
Itinerant-electron metamagnets possess an anomalous
temperature dependence of the susceptibility which increases
with temperature and then decreases after a maximum at a
finite temperature T m and usually obeys the Curie–Weiss law
at higher temperatures.80,33 It has been revealed that T m is
closely correlated with the metamagnetic transition field
H m . 86 A maximum in the temperature dependence of the
paramagnetic susceptibility has been observed for the
itinerant-band metamagnets ScCo2 , 81 YCo2 , 87,82,88 and
299
LuCo2 . 82,89 LaCoO3 also shows a temperature dependent
magnetic susceptibility with an increasing trend at low temperature and a marked maximum around 90 K followed by a
Curie–Weiss-law-like decrease at higher temperatures,8,16
which is similar to that of the itinerant metamagnets. Metamagnetic transitions have been recently reported90 for the
closely related phases Gd0.5Ba0.5CoO3 and DyCoO3 . 91
The energy needed to induce a given magnetic state is
given by the total energy difference ⌬E with respect to the
nonmagnetic case. The ⌬E versus magnetic-moment curve is
shown in Fig. 1共a兲 for LaCoO3 at 4 K. At low temperature,
the ground state of LaCoO3 corresponds to the nonmagnetic
LS state. However, the minimum of the ferromagnetic IS
state occurs about 32 meV above the LS state 关Fig. 1共a兲兴. The
existence of a ferromagnetic solution as a quasistable state
implies that a discontinuous transition in magnetization
would be possible by application of a magnetic field. This
metamagnetic IS state is destroyed by temperature as shown
in Fig. 1共b兲. In our calculation temperature is introduced via
volume expansion and hence the disappearance of IS by temperature is due to the weakening of hybridization between
Co d and O p states. Further, hole doping of LaCoO3 stabilizes the metastable state 共see Fig. 6兲. The disappearance of
the metamagnetic behavior and the appearance of ferromagnetism on hole doping in LaCoO3 can be understood as follows. The reduction in valence electrons by the Sr substitution shifts E F to the lower energy side of the valence band
toward the peak position in DOS. As a result, the Stoner
criterion for band ferromagnetism becomes fulfilled and the
metastable state is stabilized as a ferromagnetic state.
According to the FSM method, the spin-projected DOS
are filled up to E F for spin-up and spin-down electrons in
order to yield the desired externally fixed-spin magnetic moment. In effect we are dealing with a system in a uniform
magnetic field H, which maintains the magnetic moment of
the system. The difference in Fermi energy corresponds to a
difference in magnetic energy E F↑ ⫺E F↓ ⫽2 ␮ B H. Since this
difference is related to the size of the external magnetic field,
a vanishing difference corresponds to an extremum in the
magnetic total energy. Hence, this procedure allows one to
find not only stable, but also metastable magnetic states. To
obtain a better description of the metamagnetism, the variation of the difference in Fermi energy for up and down spins
(⌬E F ⫽E F↑ ⫺E F↓ ) with the magnetization, is shown in Fig. 8
for LaCoO3 at 4 K. The difference in Fermi energy is related
to the derivative of E(M ) by
⌬E F 共 M 兲 ⫽⫺2 ␮ B
␦E
.
␦M
共7兲
Stable zero-field states exist only when ⌬E F ⫽0 and its derivative ⳵ ⌬E F / ⳵ M is negative. These solutions then correspond to what one can derive by usual spin-polarized calculations. From Fig. 8 it is seen that ⌬E F (M ) nearly vanishes
at the metastable magnetic state obtained in our FSM curve.
The theoretical exploration of Wohlfarth and Rhodes76
revealed that the metamagnetic transition originates from the
sharp peak in DOS in the vicinity of E F . The metamagnetic
state in transition-metal phases is connected with the
magnetic-field-induced splitting of the majority and minority
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300
Ravindran et al.
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
attain sufficiently large values for a given applied field, a
metamagnetic transition will take place. A glance at Fig. 2共c兲
shows that a small splitting of the spin band will indeed give
large values of both D ↑ (E F ) and D ↓ (E F ). This explains the
occurrence of the metamagnetic transition in LaCoO3 .
D. Spin-state transition
FIG. 8. The difference in Fermi energy of majority and minority spin states
of LaCoO3 as a function of magnetic moment for the volume corresponding
to 4 K. The points are the calculated values and the line is a guide to the eye.
3d subbands of the transition metal. Bloch et al.92 have
pointed out that, according to the Stoner theory, E F of the
itinerant d electrons lies near a minimum or on a steep decrease in the DOS curve, so that there appears to be anomalous temperature and magnetic field dependences in the magnetic susceptibility. It is interesting to note that the DOS
curve for LaCoO3 in the LS state 关Fig. 2共c兲兴 also shows E F
in a deep valley just above the Co 3d t 2g peak. In this case
the ferromagnetic state with a rather large magnetic moment
can be approached by the applied magnetic field. This may
be the possible origin for the appearance of the metamagnetism as well as the anomalous behavior in the temperature
dependence of magnetic susceptibility.
The metamagnetic transition from paramagnetic to ferromagnetic state can be understood as follows. The applied
external field shifts the up- and down-spin bands by a small
amount. As a consequence the system gains potential energy
owing to the reduced Coulomb interaction, but at the same
time loses energy owing to an increase in the kinetic energy.
The final induced magnetic moment will be determined by
the balance between these two terms. However, in some systems there will be, for a certain critical value of the applied
field, a sudden gain in potential energy which is not sufficiently counterbalanced by the kinetic term. Hence, the
metamagnetic spin state develops.93 More quantitatively, the
criterion for the onset of metamagnetism may be written93
I
冋
1
2D ↑ 共 E F 兲
⫹
1
2D ↓ 共 E F 兲
册
⫺1
⫽1,
where I is the multiband Stoner parameter, and D ↑ (E F ) and
D ↓ (E F ) are DOS at E F for the spin-up and -down bands,
respectively. If the densities of the two state simultaneously
Despite numerous studies the nature of the spin-state
transition is still under debate. This is because in most earlier
studies a rather ionic and ligand-field-like starting point has
been assumed. Such a simplified picture does not include the
possibility of an IS state and a large e g bandwidth. The main
controversies are related to the nature of the transition, the
temperature range of the transition, and to the electronic
structure and hence to the energy levels involved. From the
temperature dependent 59Co and 139La NMR measurements
Itoh and Natori22 have shown that the anomalous behavior
around 500 K can be interpreted as a spin-state transition
between IS and HS. From electrical resistivity and neutron
diffraction measurements Thornton et al.94 concluded that
the semiconductor-to-metal transition takes place around 520
to 750 K by the stabilization of an IS state for Co3⫹ associated with a smooth transition from localized e g to itinerant
␴ * electrons. The polarized neutron-scattering experiments8
firmly supported the fact that the spin-state transition takes
place at about 90 K, which is in sharp contrast to the interpretation of x-ray absorption spectroscopy9 data, indicating
that the spin-state transition takes place in the range 400–
650 K coinciding with the gradual semiconductor-to-metal
transition. It is also suggested that the spin-state transition in
LaCoO3 occurs in two steps:8,31 first, a conversion from the
ground state LS to IS around 100 K, and second, a change
from the IS state to a mixed IS–HS state around 500 K. Our
calculations predict that the energy barrier between the LS
and IS states is 290 K and that the HS state is much higher in
energy than IS 关Fig. 1共a兲兴. So, the possibility of stabilizing
the HS state by temperature and/or hole doping is less favorable in La1⫺x Srx CoO3 . Hence, the present calculations rule
out the possibility of stabilizing mixed-spin states such as
LS–HS and IS–HS.
The energy difference between the LS and HS states of
Co3⫹ ions is reported5 to be less than 80 meV and may even
be as low as 30 meV.3 From magnetization measurements the
energy difference between the LS and HS states is reported
to be 6 –22 meV.34,7,95 Asai et al.17 estimated the energies of
the IS and HS states at 0 K to be 22.5 and 124.6 meV above
LS, respectively. Our calculated value for the energy difference between the LS and IS states is 32 meV and that between LS and HS states 1113 meV 关see Fig. 1共a兲兴. The unrestricted Hartree–Fock calculation shows that the energy of
the HS state is 35 meV higher than the LS state.35 The
Hartree–Fock calculation yields the total energy of the IS
state about 0.5 eV higher than the LS state.32 Possible reasons for the discrepancy between the two sets of results may
be that the Hartree–Fock calculations have not taken into
account the structural distortions and all possible low-energy
phases. Our recent electronic structure studies show63 that
the rhombohedral distortion is important for a correct predic-
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Ravindran et al.
J. Appl. Phys., Vol. 91, No. 1, 1 January 2002
tion of the magnetic properties of LaCoO3 共viz. calculations
predicting the cubic phase to be ferromagnetic兲. From Fig.
4共c兲, the cubic phase of LaCoO3 is found to be in a ferromagnetic IS state with a magnetic moment of 1.44 ␮ B /f.u.
and this state is 82 meV lower in energy than the nonmagnetic phase.
On going through the intermediate to high temperature
range, LaCoO3 is variously believed to be in a mixed
LS/HS,5,7,95,24,96,22,15,3,13,8,21,10 IS,96,31,27,9 mixed IS/HS,31 or
HS5,7,95,24,96,22,15,3,13,8,21,10 state. Softening of the lattice during the spin-state transition has also been observed in the
elastic modulus and this is explained by a model involving
three spin states coupled with the lattice.97 Using the LDA
⫹U approach Korotin et al.11 found that the ground state of
Co3⫹ in LaCoO3 is an LS nonmagnetic state and found two
IS states followed by an HS state at significantly higher
energy.11 Ab initio electronic structure studies on
LaCoO3 – SrCoO3 concluded that on decreasing the crystal
field LS becomes unstable, while the HS state becomes
stabilized.98 The LS-to-HS transition model needs antiferromagnetic interaction between HS Co3⫹ in order to explain
the small absolute value of the magnetic susceptibility,3,16
whereas the inelastic neutron scattering study has revealed
the presence of weak ferromagnetic correlations at
T⭓100 K.
Being a d 6 phase, LS would be more stable than HS if
the crystal field splitting of the 3d states into t 2g and e g
levels is larger than the intra-atomic exchange splitting 共i.e.,
10 Dq⬎2 J兲. Conversely, if the exchange energy dominates,
the result is an HS state with S⫽2. Owing to the degenerate
nature of the IS state with S⫽1, it is not possible to obtain
stabilization within this framework. However, if hybridization with the oxygen band is taken into account the stability
of IS can be accounted for. In Fig. 1共a兲, near degeneracy of
the LS and IS states occurs because the intra-atomic exchange splitting ⌬ ex of the S⫽1 state is close to the crystalfield splitting ⌬ cf . The present calculation shows that in the
metastable magnetic state, La, Co, and O carry moments of
0, 0.968, and 0.05 ␮ B /atom, respectively, for the experimental lattice parameters at 4 K. These values along with the
contribution from the interstitial region give a total magnetic
moment of 1.2 ␮ B /f.u.
It should be noted that our spin-polarized calculation for
LaCoO3 63 always yields a finite moment corresponding to
the flat region currently obtained from our FSM calculation
for 4 K. From the FSM curve in Fig. 1共a兲 the calculated
magnetic field necessary to stabilize an IS state is 282 T. It is
well known that Co3⫹ in the HS state has a larger ionic
radius than in the LS state, and LS–HS transitions are probably accompanied by an increase in volume. Keeping those
features in mind we carried out the calculations for the electronic structure of LaCoO3 with the lattice parameters for
1248 K, which can imitate the influence of the temperature
via thermal expansion. Figure 1共b兲 shows the total energies
as a function of magnetic moment for the expanded lattice.
The HS state (M ⫽4 ␮ B ) lies much higher in energy than LS
and IS at low as well as high temperature, indicating that it is
less probable to stabilize the HS state by temperature/hole
doping. However, our FSM calculations show that an IS state
301
is always lower in energy than the HS state for hole doped
LaCoO3 . So, theory rules out the possibility of stabilizing
HS by either temperature or hole doping. Hence, the LSto-IS spin-state transition is the more probable transition in
LaCoO3 .
IV. SUMMARY
The electronic structure and magnetic properties of
LaCoO3 as a function of hole doping and temperature have
been studied with the fixed-spin procedure using the
generalized-gradient-corrected FLAPW method. The holedoping effect has been simulated by VCA as well as through
supercell calculations. From these studies the following conclusions have been arrived at.
共i兲 The nonmagnetic solution with Co3⫹ in the LS state
has the lowest total energy at low temperature and this is
consistent with the experimental observations.
共ii兲 The FSM calculation suggests that the first excited
state configuration in LaCoO3 is an IS state which lies only
32 meV higher than the LS state. It is experimentally established that there is a transition from an LS nonmagnetic state
to a magnetic state with increasing temperature. As this transition is experimentally reported to be around 90 K, we ascribe the nonmagnetic-to-magnetic transition in LaCoO3 to
the LS–IS transition. Theoretical results along with the experimental findings lead us to the conclusion that the transition near 500 K is not a spin transition, but rather a
semiconductor-to-metal transition and/or a localized-toitinerant electron transition.
共iii兲 The IS state is very sensitive to the volume and it
becomes unfavorable at a volume corresponding to the experimental volume at 1248 K.
共iv兲 The HS state is expected to have a moment of 4
␮ B /Co3⫹ within the ionic picture which is much higher in
energy than the IS state at 4 K as well as at 1248 K. Hence,
the possible spin-state transition in LaCoO3 is from LS to IS,
and theory predicts that the stabilization of the HS state in
LaCoO3 is less probable.
共v兲 We find that the energy barriers between LS and
HS as well as between IS and HS are very large. Our supercell calculations on hole doped LaCoO3 also show that the
Co ions closer to La and Sr have almost the same spin polarization. Hence theory rules out the possibility of stabilizing a mixed-spin state such as LS and HS, IS and HS or the
combination of these by temperature/hole doping.
共vi兲 The hole doping effect induces ferromagnetism in
LaCoO3 , which originates from the filling of Co t 2g levels
and as a result the IS state becomes stabilized over the LS
state. The calculated magnetic moment for the equilibrium
state as a function of hole doping is found to be in good
agreement with the low temperature neutron diffraction and
susceptibility data.
共vii兲 With equilibrium lattice parameters, our calculations predict the possibility of a metamagnetic transition.
Hence the experimentally observed anomalous behavior in
the temperature dependent susceptibility has been interpreted
as a metamagnetic transition from a nonmagnetic LS to a
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302
ferromagnetic IS state. The critical field for the metamagnetic transition is estimated from the FSM curve of LaCoO3
to be 282 T.
ACKNOWLEDGMENTS
P.R. is grateful for financial support from the Research
Council of Norway. Part of these calculations were carried
out on the Norwegian supercomputer facilities. He is also
grateful to Professor B. Johansson, Professor O. Eriksson,
and Dr. Lars Nordström for fruitful discussions and R. Vidya
for comments and a critical reading of the manuscript.
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